Simplify the following expression and state the condition under which the simplification is valid. $x = \dfrac{y^2 - 16}{y + 4}$
Answer: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = y$ $ b = \sqrt{16} = 4$ So we can rewrite the expression as: $x = \dfrac{({y} + {4})({y} {-4})} {y + 4} $ We can divide the numerator and denominator by $(y + 4)$ on condition that $y \neq -4$ Therefore $x = y - 4; y \neq -4$